1. Consider a cubic infinite potential well of length L. (Assume that the particle is confined to stay withing 0 and L in all the directions.)
(a) What is the ground state energy and the ground state wavefunction?
(b) What is the next energy level? Are there more than one wavefunction with the same energy? If there are then write down the quantum numbers for all the degenerate states.
2. Write down the energies of the next 5 levels and the quantum numbers for all degenerate energy eigenstates.